When are A3, H3 and A6, H6 not 'wasted moves'?

I've heard that masters think that pushing the far pawns forward, defensively, to prevent attacks from the bishop and knight to the center a waste of tempo.  

They show that attacks like fried liver can be prevented in other ways (in a well-ordered opening), I guess by castling or  by pushing a pawn up to fork the bishop and pawn of the opponent and trade your knight for their bishop (pxp, bxk, qxb). But the latter can lead to some messy and risky conflicts.  And sometimes I pull the opposite knight out instead so I'm stuck doing H3, when the threat of fried liver looms.

When are those corner pawn moves a good idea and when are they just a waste of time?

One situation where they can be good: if you have a space advantage. Often if White has a space advantage, he doesn't want to trade pieces, so stopping a bishop coming to g4 and pinning the knight, with the idea of trading next turn, might be a good idea.

Another situation is if the squares in the centre need the control of a piece ie. if Black's strategy is to control the dark squares like d4 and e5 and White protects them with a knight on f3, then Black might often play Bg4 to try and exchange off the knight. Here's an example of that:

Whenever they do something.

ever heard of the Najdorf?..

Ask yourself if an opponent's piece can come to g4/b4/g5/b5. If yes, ask yourself if you really care. In the above examples, there's a specific reason that allowing Bg4 and Bxf3 is bad; the knight is serving a specific and important purpose--more important than having the bishop pair. 

Sometimes you're trying to prevent knights from hopping in, or just denying the square in general, and that's okay if it's part of your overall strategy, or there's a specific move you're trying to prevent. 

I play the Leningrad Dutch, which involves black playing ..f5, ..g6, ..d6, ..Nf6, ..Bg7 and ..0-0. This leaves the a2-g8 diagonal (and particularly f7 and e6) very weak. Thus, I always have to be careful of Bc4+ and Qb3+ type moves. White invariably playes Nf3 at some point, and from there can play Ng5 at some point to further attack the f7 and e6 squares. If I allow Ng5 and only then play h6, it's possible white already can play Bc4+. Kh8 is impossible in some positions because of Nf7+ either forking a king and queen (probably winning an exchange that I'd have to give up instead) or maybe even making a windmill. See diagram for an example (sorry if there's some other tactical opportunity present, just whipped it up for a visual aid).

^the memories of what happened to me on the a2-g8 diagonal back when I played the leningrad still make me cringe *shivers*.

Worthwhile reading, thanks!